Methods and systems for determining bulk density, porosity, and pore size distribution of subsurface formations

ABSTRACT

Herein methods and systems for determining matrix or grain density of a subsurface formation are described. This includes measuring in-air mass of a fluid-saturated sample of the subsurface formation, wherein the in-air mass comprises mass of matrix or grains of the sample, mass of a fluid surrounding the sample, and mass of the fluid inside the sample. The volume of the fluid inside the sample, V ϕ , and volume of the fluid surrounding the sample, V sur , are determined using nuclear magnetic resonance (NMR). The fluid-saturated sample can then be submerged in a predetermined volume of a weighing fluid and mass of the fluid-saturated sample without the surrounding fluid in the weighing fluid, m f  is measured. Using the measured and determined values one can determine the volume of the sample without the surrounding fluid, V c , the bulk density of the fluid-saturated sample without the surrounding fluid, ρ b , the volume of the matrix, V m , and the matrix or grain density of the subsurface formation, ρ m .

RELATED APPLICATIONS

This application is a continuation of and claims priority to U.S. patentapplication Ser. No. 15/673,996 filed on Aug. 10, 2017 titled “METHODSAND SYSTEMS FOR DETERMINING BULK DENSITY, POROSITY, AND PORE SIZEDISTRIBUTION OF SUBSURFACE FORMATIONS,” which is hereby incorporatedherein by reference in its entirety.

TECHNICAL FIELD

Embodiments relate to reservoir evaluation. More specifically, exampleembodiments relate to methods and systems for determining bulk density,porosity, and pore size distribution of subsurface formations. Thesemethods and systems utilize a combination of (Nuclear MagneticResonance) NMR and gravimetric techniques.

BACKGROUND

Bulk density is one of the most important parameters in reservoirevaluation. It is widely used for estimation of reserves of hydrocarbonsin reservoirs. Traditionally, well logs and core measurements are thetwo approaches to obtain key petrophysical parameters for reservoirevaluation and description. These measurements are expensive and manytimes they require extra rig time, which is also very expensive.

For example, bulk density can be measured in real time with loggingwhile drilling (LWD) density log or can be measured using wireline (WL)density log. Both use a gamma ray source and measure the attenuatedgamma ray coming to the detector after interacting with the formation.Generally speaking, the LWD density measurement represents the bulkdensity of the rock with the formation fluids in the pore space, whereasthe WL density measures the bulk density of the rock with invadedfluids; for low permeable unconventional rocks, the difference should beminimal. Bulk density can be precisely measured using core plugs whenthey are available.

Obtaining accurate petrophysical parameters from drill cuttings isbeneficial and desirable for at least two reasons. First, drill cuttingsare readily available from any drilled well and thus does not add extrarig time or extra cost to the operation. Second, measurement can be doneat the wellsite and offers data for real-time operational decisions,such as drilling and the succeeding hydraulic fracturing.

However, it is a challenge to measure the volume of the cuttingaccurately as it is hard to remove the fluid on the surface of thecutting. The traditional sample preparation method uses a damp papertowel to remove the excess fluid from the surface, and due to theirregular shape of the surface features, the validity of the totalremoval of the surface fluid is always questionable. Moreover, if thepaper towel is too dry, the fluid within the cutting sample can be lostdue to capillary force.

SUMMARY

Example embodiments disclosed herein relate to improved methods andsystems for determining bulk density, porosity, and pore sizedistribution of subsurface formations.

One example embodiment is a method for determining matrix or graindensity of a subsurface formation. The method includes measuring anin-air mass of a fluid-saturated sample of the subsurface formation,wherein the in-air mass includes mass of the matrix or grains of thesample, mass of a fluid surrounding the sample, and mass of the fluidinside the sample. The in-air mass of the fluid-saturated sample, ms,may be given by the formula

m _(s) =V _(m)ρ_(m)+(V _(ϕ) +V _(sur))ρ_(l)

where ρ_(m) is a density of the matrix of the subsurface formation,ρ_(l) is a density of the fluid inside and surrounding the sample, V_(m)is a volume of the matrix, V_(ϕ) is a volume of the fluid inside thesample, and V_(sur) is a volume of the fluid surrounding the sample. Themethod also includes separately determining the volume of the fluidinside the sample, V_(ϕ), and the volume of the fluid surrounding thesample, V_(sur), using nuclear magnetic resonance (NMR). The method mayfurther include placing the sample in a predetermined volume of aweighing fluid, and measuring mass of the fluid-saturated sample in theweighing fluid. The mass of the fluid-saturated sample without thesurrounding fluid in the weighing fluid, m_(f), may be given by theformula

m _(f) =V _(m)ρ_(m) +V _(ϕ)ρ_(l) −V _(c)ρ_(f)

where ρ_(f) is the density of the weighing fluid. The method may furtherinclude determining a volume of the fluid-saturated sample without thesurrounding fluid, V_(c), using the formula

V _(c)=(m _(s) −m _(f) −V _(sur)ρ_(l))/ρ_(f).

The method may also include determining a bulk density of thefluid-saturated sample without the surrounding fluid, ρ_(b), using theformula

$\rho_{b} = {\frac{{V_{m}\rho_{m}} + {V_{\varphi}\rho_{l}}}{m_{s} - m_{f} - {V_{sur}\rho_{f}}}{\rho_{f}.}}$

The method may further include determining the volume of the matrix,V_(m), using the formula

V _(m)=(m _(s) −m _(f) −V _(sur)ρ_(f))/ρ_(f) −V _(ϕ).

The method may also include determining the matrix or grain density ofthe subsurface formation, ρ_(m), using the formula

$\rho_{m} = {\frac{m_{s} - {\left( {V_{\varphi} + V_{sur}} \right)\rho_{f}}}{{\left( {m_{s} - m_{f} - {V_{sur}\rho_{f}}} \right)/\rho_{f}} - V_{\varphi}}.}$

Another example embodiment relates to computer programs stored incomputer readable media. The non-transitory computer-readable media mayhave, for example, computer executable instructions that trigger thecomputer to perform the operation of receiving in-air mass of afluid-saturated sample of the subsurface formation, wherein the in-airmass includes mass of the matrix or grains of the sample, mass of afluid surrounding the sample, and mass of the fluid inside the sample.The in-air mass of the fluid-saturated sample, m_(s), may be given bythe formula

m _(s) =V _(m)ρ_(m)+(V _(ϕ) +V _(sur))ρ_(l)

where ρ_(m) is a density of the matrix of the subsurface formation,ρ_(l) is a density of the fluid inside and surrounding the sample, V_(m)is a volume of the matrix, V_(ϕ) is a volume of the fluid inside thesample, and V_(sur) is a volume of the fluid surrounding the sample. Thecomputer executable instructions may also trigger the computer todetermine the volume of the fluid inside the sample, V_(ϕ), and volumeof the fluid surrounding the sample, V_(sur), from NMR measurements. Thecomputer executable instructions may also trigger the computer toreceive the mass of the fluid-saturated sample in a weighing fluid. Themass of the fluid-saturated sample without the surrounding fluid in theweighing fluid, m_(f), may be given by the formula

m _(f) =V _(m)ρ_(m) +V _(ϕ)ρ_(l) −V _(c)ρ_(f)

where ρ_(f) is the density of the weighing fluid. The computerexecutable instructions may also trigger the computer to calculate avolume of the fluid-saturated sample without the surrounding fluid,V_(c), using the formula

V _(c)=(m _(s) −m _(f) −V _(sur)ρ_(l))/ρ_(f).

The computer executable instructions may further trigger the computer tocalculate a bulk density of the fluid-saturated sample without thesurrounding fluid, ρ_(b), using the formula

$\rho_{b} = {\frac{{V_{m}\rho_{m}} + {V_{\varphi}\rho_{l}}}{m_{s} - m_{f} - {V_{sur}\rho_{f}}}{\rho_{f}.}}$

The computer executable instructions may further trigger the computer tocalculate the volume of the matrix, V_(m), using the formula

V _(m)=(m _(s) −m _(f) −V _(sur)ρ_(f))/ρ_(f) −V _(ϕ).

The computer executable instructions may further trigger the computer tocalculate the matrix or grain density of the subsurface formation,ρ_(m), using the formula

$\rho_{m} = {\frac{m_{s} - {\left( {V_{\varphi} + V_{sur}} \right)\rho_{f}}}{{\left( {m_{s} - m_{f} - {V_{sur}\rho_{f}}} \right)/\rho_{f}} - V_{\varphi}}.}$

Another example embodiment is a system for determining matrix or graindensity of a subsurface formation. The system may include afluid-saturated sample of the subsurface formation, and a weighingbalance, which may be configured to receive the fluid-saturated sampleand output the in-air mass and in-fluid mass of the sample. The systemmay also include a computer having one or more processors and anon-transitory computer readable medium, which may include computerexecutable instructions that when executed by the one or moreprocessors, trigger the computer to fetch in-air mass of thefluid-saturated sample of the subsurface formation from the weighingscale. The in-air mass may include mass of the matrix or grains of thesample, mass of a fluid surrounding the sample, and mass of the fluidinside the sample. The in-air mass of the fluid-saturated sample, m_(s),may be given by the formula

m _(s) =V _(m)ρ_(m)+(V _(ϕ) +V _(sur))ρ_(l)

where ρ_(m) is a density of the matrix of the subsurface formation,ρ_(l) is a density of the fluid inside and surrounding the sample, V_(m)is a volume of the matrix, V_(ϕ) is a volume of the fluid inside thesample, and V_(sur) is a volume of the fluid surrounding the sample. Thesystem may also include an NMR, which may be operably connected to thecomputer and configured to determine the volume of the fluid inside thesample, V_(ϕ), and volume of the fluid surrounding the sample, V_(sur),using NMR. The computer may be configured to receive the volume of thefluid inside the sample, V_(ϕ), and volume of the fluid surrounding thesample, V_(sur), from the NMR, and the mass of the fluid-saturatedsample in a weighing fluid from the weighing scale. The mass of thefluid-saturated sample without the surrounding fluid in the weighingfluid, m_(f), may be given by the formula

m _(f) =V _(m)ρ_(m) +V _(ϕ)ρ_(l) −V _(c)ρ_(f)

where ρ_(f) is the density of the weighing fluid. The computerexecutable instructions may also trigger the computer to determine avolume of the fluid-saturated sample without the surrounding fluid,V_(c), using the formula

V _(c)=(m _(s) −m _(f) −V _(sur)ρ_(l))/ρ_(f).

The computer executable instructions may further trigger the computer todetermine a bulk density of the fluid-saturated sample without thesurrounding fluid, ρ_(b), using the formula

$\rho_{b} = {\frac{{V_{m}\rho_{m}} + {V_{\varphi}\rho_{l}}}{m_{s} - m_{f} - {V_{sur}\rho_{f}}}{\rho_{f}.}}$

The computer executable instructions may further trigger the computer todetermine the volume of the matrix, V_(m), using the formula

V _(m)=(m _(s) −m _(f) −V _(sur)ρ_(f))/ρ_(f) −V _(ϕ).

The computer executable instructions may further trigger the computer todetermine the matrix or grain density of the subsurface formation,ρ_(m), using the formula

$\rho_{m} = {\frac{m_{s} - {\left( {V_{\varphi} + V_{sur}} \right)\rho_{f}}}{{\left( {m_{s} - m_{f} - {V_{sur}\rho_{f}}} \right)/\rho_{f}} - V_{\varphi}}.}$

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 illustrates an example sample or drill cutting of a subsurfaceformation, according to one example embodiment of the disclosure.

FIG. 2 illustrates an example apparatus for determining in-air mass of afluid-saturated sample of a subsurface formation, according to oneexample embodiment of the disclosure.

FIG. 3 illustrates example NMR spectra of a sample from a subsurfaceformation with varying amounts of washing fluid added, according to oneexample embodiment of the disclosure.

FIG. 4 illustrates an example graph showing NMR results of a sample of asubsurface formation, according to some example embodiments of thedisclosure.

FIG. 5 illustrates example NMR spectra (one spectrum in incremental andthe other in cumulative) of a sample from a subsurface formation withoutany extra fluid added, according to one example embodiment of thedisclosure.

FIG. 6 illustrates an example graph showing NMR results of a sample of asubsurface formation, according to one example embodiment of thedisclosure.

FIG. 7 illustrates an example of NMR results from a sample of asubsurface formation with extra fluid added (1.5 ml for this example),according to one example embodiment of the disclosure.

FIG. 8 illustrates an example graph showing NMR results from a sample ofa subsurface formation, according to one example embodiment of thedisclosure.

FIG. 9 illustrates an example apparatus for determining in-fluid mass ofa fluid-saturated sample of a subsurface formation, according to someexample embodiments of the disclosure.

FIG. 10 illustrates example steps in a method for determining matrix orgrain density of a subsurface formation, according to some exampleembodiments of the disclosure.

FIG. 11 is an example computer set up for determining matrix or graindensity of a subsurface formation, according to some example embodimentsof the disclosure.

FIG. 12 is an example system for determining matrix or grain density ofa subsurface formation, according to some example embodiments of thedisclosure.

DETAILED DESCRIPTION

Example embodiments disclosed propose a method to measure and analyzedrill cuttings using a combination of nuclear magnetic resonance (NMR)measurements and mass measurements in-air and in-fluid to obtainmultiple key petrophysical parameters accurately with little samplepreparation. Example embodiments present a new and accurate method tomeasure the bulk density using saturated drill cuttings, which arereadily available for any drilled hydrocarbon well. The method combinesNMR and gravimetric techniques, and the results include bulk density,grain density, porosity, and pore-size distribution of the drillcuttings.

Turning now to the figures, FIG. 1 illustrates a sample 10, such as adrill cutting of a subsurface formation, such as from a hydrocarbonreservoir. In an exemplary method, the first step is to collect drillcuttings 10 that are representative of the subsurface formation. Thenext step is to size-sort as to eliminate particles of large size, whichare normally from caving, and to eliminate particles of too small asize, which may have circulated multiple times through the up-hole anddown-hole cycles with the drilling mud. In some embodiments, at leastone dimension of the fluid-saturated sample may be about 0.5 mm to 3 mm.These limits, however, can be adjusted according to the specificformation and the bits used for drilling.

Additionally, the collected cuttings may be washed using sufficientfluid such that it minimizes the impact of small particles from drillingmud that stick to the cutting surface or in the surrounding fluid whichcan impact both mass measurements and NMR measurements. Washing may alsobenefit other subsequent measurements, such as gamma-ray measurement, onthe drill cuttings because the effect of the small particles on thegamma ray measurements can be significant.

The figure on the left in FIG. 1, denoted A, illustrates a drillcuttings chip 10 with fluid 30 on the surface, with a volume of V_(sur).The volume of the cutting inside the fluid envelope can be given asV_(c). The figure on the right in FIG. 1, denoted B, is a magnifiedportion of the interior of the cutting chip 10 consisting of matrixgrains 20 (may be in spheres or other geometric shapes) with volume ofV_(m) and density of ρ_(m), and pore space 15, with volume of V_(Φ) andfilled by a fluid with a density of ρ_(l).

The next step of the method is to measure the in-air mass of thecollected drill cutting 10. FIG. 2, for example, illustrates anapparatus, such as a weighing balance 25 with a support device 12 thatmay be used to measure the in-air mass of the cutting sample 10. Thein-air mass includes mass of the matrix or grains of the sample, mass ofa fluid surrounding the sample, and mass of the fluid inside the sample.The in-air mass of the fluid-saturated sample, m_(s), may be given bythe formula

m _(s) =V _(m)ρ_(m)+(V _(ϕ) +V _(sur))ρ_(l)

where ρ_(m) is a density of the matrix of the subsurface formation,ρ_(l) is a density of the fluid inside and surrounding the sample, V_(m)is a volume of the matrix, V_(ϕ) is a volume of the fluid inside thesample, and V_(sur) is a volume of the fluid surrounding the sample.

The next step is to separately determine volume of the fluid inside thesample, V_(ϕ), and volume of the fluid surrounding the sample, V_(sur),using nuclear magnetic resonance (NMR). To clearly separate the NMRsignals for liquid inside and surrounding the cuttings, a sufficientamount of surrounding fluid may be used one time or in a step-wisefashion. Due to the clay sensitivity issues, many wells inunconventional plays are drilled using oil based mud (OBM). The exampleembodiments disclosed propose a new method to separate the NMR signal ofthe fluid on the cuttings surfaces and the fluids from the interiorpores of the cutting samples based on two assumptions: (1) fluids insidethe shale cuttings have short relaxation time, and (2) fluid from OBMhas a longer T₂, even in the presence of cuttings.

FIG. 3 illustrates an example graph 35 showing NMR readings (spectra) asample of a subsurface formation with varying fluid content added to thesample, according to one example embodiment of the disclosure. A seriesof NMR experiments may be performed on the cutting sample and a T₂incremental distribution spectra may be obtained as shown in FIG. 3, forexample. A known amount of the drilling fluid, diesel for example, canbe gradually added to the cutting sample and measurement may be made,e.g., “1.5 ML DIESEL Inc.” stands for the incremental T₂ distributioncurve after 1.5 ml diesel was added to the original cutting sample. Twomodes of T₂ distribution may be noted, for example, a bigger one around25 ms representing the free fluid, and a smaller peak below 1 msrepresenting the fluid inside the cutting samples.

A series of NMR experiments with cuttings demonstrate that the modeposition of the T₂ signal of the OBM outside the cuttings does move tolonger relaxation times as more fluid is gradually added (FIG. 3), andstops moving when the volume of added fluid is relatively large comparedto the original amount of fluid on the surface. It should also be notedseparation and quantification of the liquid inside the cuttings when alarge amount of drilling fluid is present is attainable as there are twomodes of T₂ distribution (FIG. 3). A larger peak around 25 msrepresenting the free fluid outside the cuttings, and a smaller peakbelow 1 ms representing the fluid inside the cutting samples. On the topcurve (1.5 ml diesel inc., where the word ‘inc.’ stands for incrementalT₂ distribution), the two modes are more clearly separated than thebottom curve (as received, i.e. no extra diesel is added).

FIG. 4 illustrates an example graph 40 of the total amount of fluidmeasured by NMR (vertical axis) versus the extra fluid added to thecutting sample in ml (horizontal axis). It can be seen from the graphthat line 45 intercepts with the vertical axis just above 1, and this isthe total amount of fluid on the surface of and inside the cuttingsample prior to the addition of diesel. FIG. 5 shows a graph 50 with noextra fluid added; a single point method of separation of V_(sur) andV₁₀₁ . Here it can be seen that the cumulative volume 52 of T₂distribution of fluid from NMR measurement (scale on the right) and theincremental volume 53 of fluid (scale on the left) from NMR measurementare plotted.

No additional fluid is added in this variation of the method. A cut off51 is selected from the incremental T₂ distribution line (a verticaldotted line drawn at the trough on the incremental curve in FIG. 5, thevolume to the left of which represents the fluid volume inside thecuttings and to the right of which represents the volume on the surface,or bulk volume movable (BVM) when more fluid is added). The total volumeof the fluid inside the cuttings (54, dashed line) can be read from thecumulative curve 52 and the volume on the surface of the cuttings is thedifference between the total and the volume inside the cuttings (V_(sur)in FIG. 5, or BVM on experiments when known amount of extra fluid isadded)

In case where excess fluid is present a plot can be graphed as seen inFIG. 6. Similar to line 45 shown in FIG. 4, line 65 in graph 60 shown inFIG. 6 illustrates that the BVM volume measurement from NMR increases asextra fluid is added to the cutting sample. Graph 60 shows a multi-pointmeasurement from BVM to separate V_(sur) and V_(Φ), i.e. BVM vs. amountsof fluid added to the cutting sample. The intercept of the regressionline 65 shows the volume of fluid on the surface of the cuttings(V_(sur) is the intercept of the regression line, i.e. 1.0073 ml forthis example).

FIG. 7 illustrates another example graph 70 where 1.5 ml of fluid isadded to the sample. Again both cumulative volume 75 of T₂ distribution(scale on the right) of fluid from NMR measurement and the incrementalvolume 72 (scale on the left) of T₂ distribution of fluid from NMRmeasurement are plotted. From the incremental volume 72 (scale on theleft) of T₂ distribution curve, the mean of the bulk volume movable canbe found, labeled as “T_(2BVM)”. When various amounts of fluid are addedto the sample, a series of “T_(2BVM)” values can be acquired in a methodoutlined here or other methods similar to the method outlined here, andthe use of “T_(2BVM)” is shown in FIG. 8. Graph 80 shown in FIG. 8illustrates a third way to get the amount of the fluid on the surface ofcuttings, V_(sur), using the T_(2BVM) value. The negative of theintercept of the regression line 85 is the volume of fluid on thesurface of the samples (V_(sur) is the negative intercept of theregression line, i.e. 1.00222 ml for this example, where T_(2bulkmud) isthe T₂ relaxation time of the fluid (maybe the drilling fluid or others)to rinse the sample with.

The next step is to measure the sample mass in a weighing fluid. FIG. 9illustrates an experimental set up 90 including an apparatus 25 formeasuring the in-fluid mass of the sample, according to one exampleembodiment. In this example, the fluid-saturated sample 10 may be placedin a weighing fluid 94, and the weighing scale 25 may be used to measurethe in-fluid mass of the sample 10. The weighing fluid can be thedrilling fluid, or a fluid with gravimetric properties similar to thedrilling fluid. In one example embodiment, the weighing fluid is diesel.

The mass of the sample in the weighing fluid, m_(f), may be given by theformula

m _(f) =V _(m)ρ_(m) +V _(ϕ)ρ_(l) −V _(c)ρ_(f)

where ρ_(f) is the density of the weighing fluid. From the combinationof two mass measurements and NMR measurement, multiple key parameterscan be obtained as outlined in the following sections for reservoircharacterization. These parameters include porosity, cutting totalvolume, bulk density, and matrix/grain density. For example, the methodmay further include determining a volume of the fluid-saturated samplewithout the surrounding fluid, V_(c), using the formula

V _(c)=(m _(s) −m _(f) −V _(sur)ρ_(l))/ρ_(f).

In the next step, the method may also include determining a bulk densityof the fluid-saturated sample without the surrounding fluid, ρ_(b),using the formula

$\rho_{b} = {\frac{{V_{m}\rho_{m}} + {V_{\varphi}\rho_{l}}}{m_{s} - m_{f} - {V_{sur}\rho_{f}}}{\rho_{f}.}}$

In the next step, the method may further include determining the volumeof the matrix, V_(m), using the formula

V _(m)=(m _(s) −m _(f) −V _(sur)ρ_(f))/ρ_(f) −V _(ϕ).

As a last step, the method may include determining the matrix or graindensity of the subsurface formation, ρ_(m), using the formula

$\rho_{m} = {\frac{m_{s} - {\left( {V_{\varphi} + V_{sur}} \right)\rho_{f}}}{{\left( {m_{s} - m_{f} - {V_{sur}\rho_{f}}} \right)/\rho_{f}} - V_{\varphi}}.}$

These measurements can be performed on the cutting samples along theentirety of the drilled well and, thus, data can be obtained to evaluatethe heterogeneity of the vertical or horizontal wells. This couldpotentially be used in real time to optimize the number and placement offrac stages for unconventional reservoirs.

Here, the contribution of the sample support device (12 in FIG. 1) isneglected, as the sample support device is chosen so the volume isminimum compared to the volume of the cuttings. There are three types offluids involved in the drill cuttings analysis: the fluid inside thecutting samples, the drilling fluid, and the weighing fluid. At wellsite, depending on the permeability of the rock, the fluid inside can bereplaced by the drilling fluid to various degrees. For example, forcuttings of unconventional rocks, it is likely that the fluid on thesurface of the cuttings is different from the fluid inside, whereas forcuttings of very permeable rocks, the original fluid inside the cuttingsis replaced by the drilling fluid rather quickly. If we choose thedrilling fluid as the weighing liquid, the most complicated situationinvolves two types of fluids: the original fluid inside the pores andthe drilling fluid. In the case where all three fluids are the same forhigh permeable rocks, the following calculations may be simplified evenfurther. The following calculation uses two types of fluids as anexample.

FIG. 10 illustrates an example method 100 for determining matrix orgrain density of a subsurface formation. The method includes measuringin-air mass of a fluid-saturated sample of the subsurface formation instep 102, wherein the in-air mass includes mass of the matrix or grainsof the sample, mass of a fluid surrounding the sample, and mass of thefluid inside the sample. The in-air mass of the fluid-saturated sample,m_(s), may be given by the formula

m _(s) =V _(m)ρ_(m)+(V _(ϕ) +V _(sur))ρ_(l)

where ρ_(m) is a density of the matrix of the subsurface formation,ρ_(l) is a density of the fluid inside and surrounding the sample, V_(m)is a volume of the matrix, V_(ϕ) is a volume of the fluid inside thesample, and V_(sur) is a volume of the fluid surrounding the sample. Themethod also includes separately determining volume of the fluid insidethe sample, V_(ϕ), and volume of the fluid surrounding the sample,V_(sur), using nuclear magnetic resonance (NMR), at step 104. The methodmay further include placing the sample in a predetermined volume of aweighing fluid at step 106, and measuring the mass of thefluid-saturated sample in the weighing fluid, at step 108. The mass ofthe fluid-saturated sample without the surrounding fluid in the weighingfluid, m_(f), may be given by the formula

m _(f) =V _(m)ρ_(m) +V _(ϕ)ρ_(l) −V _(c)ρ_(f)

where ρ_(f) is the density of the weighing fluid. At step 110, themethod may further include determining a volume of the fluid-saturatedsample without the surrounding fluid, V_(c), using the formula

V _(c)=(m _(s) −m _(f) −V _(sur)ρ_(l))/ρ_(f).

The method may also include determining a bulk density of thefluid-saturated sample without the surrounding fluid, ρ_(b), using theformula

$\rho_{b} = {\frac{{V_{m}\rho_{m}} + {V_{\varphi}\rho_{l}}}{m_{s} - m_{f} - {V_{sur}\rho_{f}}}{\rho_{f}.}}$

At step 112, the method may further include determining the volume ofthe matrix, V_(m), using the formula

V _(m)=(m _(s) −m _(f) −V _(sur)ρ_(f))/ρ_(f) −V _(ϕ).

Finally, at step 114, the method may include determining the matrix orgrain density of the subsurface formation, ρ_(m), using the formula

$\rho_{m} = {\frac{m_{s} - {\left( {V_{\varphi} + V_{sur}} \right)\rho_{f}}}{{\left( {m_{s} - m_{f} - {V_{sur}\rho_{f}}} \right)/\rho_{f}} - V_{\varphi}}.}$

Computer Readable Medium

Another example embodiment relates to computer programs stored incomputer readable media. Referring to FIG. 11, the foregoing process asexplained with reference to FIGS. 1-10 can be embodied incomputer-readable code. The code can be stored on, e.g., anon-transitory computer readable medium, such as a floppy disk 164,CD-ROM 162, which may be read by disk drives 156, 158, or a magnetic (orother type) hard drive 160 forming part of a general purposeprogrammable computer. The computer, as known in the art, includes acentral processing unit 150, a user input device such as a keyboard 154,and a user display 152 such as a flat panel LCD display or cathode raytube display. According to this embodiment, the computer readable medium160, 162, 164 includes logic operable to trigger the computer to executeacts as set forth above and explained with respect to the previousfigures. The non-transitory computer-readable medium 160, 162, 164 mayhave, for example, computer executable instructions that trigger thecomputer to perform the operations of receiving in-air mass of afluid-saturated sample of the subsurface formation, wherein the in-airmass includes mass of the matrix or grains of the sample, mass of afluid surrounding the sample, and mass of the fluid inside the sample.The in-air mass of the fluid-saturated sample, m_(s), may be given bythe formula

m _(s) =V _(m)ρ_(m)+(V _(ϕ) +V _(sur))ρ_(l)

where ρ_(m) is a density of the matrix of the subsurface formation,ρ_(l) is a density of the fluid inside and surrounding the sample, V_(m)is a volume of the matrix, V_(ϕ) is a volume of the fluid inside thesample, and V_(sur) is a volume of the fluid surrounding the sample. Thecomputer executable instructions may also trigger the computer todetermine volume of the fluid inside the sample, V_(ϕ), and volume ofthe fluid surrounding the sample, V_(sur), using nuclear magneticresonance (NMR). The computer executable instructions may also triggerthe computer to receive mass of the fluid-saturated sample in a weighingfluid. The mass of the fluid-saturated sample without the surroundingfluid in the weighing fluid, m_(f), may be given by the formula

m _(f) =V _(m)ρ_(m) +V _(ϕ)ρ_(l) −V _(c)ρ_(f)

where ρ_(f) is the density of the weighing fluid. The computerexecutable instructions may also trigger the computer to determine avolume of the sample without the surrounding fluid, V_(c), using theformula

V _(c)=(m _(s) −m _(f) −V _(sur)ρ_(l))/ρ_(f).

The computer executable instructions may further trigger the computer todetermine a bulk density of the fluid-saturated sample without thesurrounding fluid, ρ_(b), using the formula

$\rho_{b} = {\frac{{V_{m}\rho_{m}} + {V_{\varphi}\rho_{l}}}{m_{s} - m_{f} - {V_{sur}\rho_{f}}}{\rho_{f}.}}$

The computer executable instructions may further trigger the computer todetermine the volume of the matrix, V_(m), using the formula

V _(m)=(m _(s) −m _(f) −V _(sur)ρ_(f))/ρ_(f) −V _(ϕ).

The computer executable instructions may further trigger the computer todetermine the matrix or grain density of the subsurface formation,ρ_(m), using the formula

$\rho_{m} = {\frac{m_{s} - {\left( {V_{\varphi} + V_{sur}} \right)\rho_{f}}}{{\left( {m_{s} - m_{f} - {V_{sur}\rho_{f}}} \right)/\rho_{f}} - V_{\varphi}}.}$

Example System

Another example embodiment is a system 1200 for determining matrix orgrain density of a subsurface formation. The system 1200 may include afluid-saturated sample 10 of the subsurface formation, as illustrated inFIGS. 1, 2, and 9. The system 1200 may also include a weighing scale 25,as illustrated in FIGS. 2 and 9, which may be configured to receive thefluid-saturated sample 10 and output the in-air mass and in-fluid massof the sample 10. The system 1200 may also include a computer 200 havingone or more processors 150 and a non-transitory computer readable medium160, which may include computer executable instructions that whenexecuted by the one or more processors 150, trigger the computer 200 toreceive in-air mass of the fluid-saturated sample 10 of the subsurfaceformation from the weighing scale 25. The in-air mass may include massof the matrix or grains of the sample, mass of a fluid surrounding thesample, and mass of the fluid inside the sample. The in-air mass of thefluid-saturated sample, m_(s), may be given by the formula

m _(s) =V _(m)ρ_(m)+(V _(ϕ) +V _(sur))ρ_(l)

where ρ_(m) is a density of the matrix of the subsurface formation,ρ_(l) is a density of the fluid inside and surrounding the sample, V_(m)is a volume of the matrix, V_(ϕ) is a volume of the fluid inside thesample, and V_(sur) is a volume of the fluid surrounding the sample. Thesystem 1200 may also include a NMR device 500, which may be operablyconnected to computer 200 and configured to determine the volume of thefluid inside the sample, V_(ϕ), and volume of the fluid surrounding thesample, V_(sur), using nuclear magnetic resonance (NMR). The computer200 may be configured to receive the volume of the fluid inside thesample, V_(ϕ), and volume of the fluid surrounding the sample, V_(sur),from the NMR device 500, and the mass of the fluid-saturated sample in aweighing fluid from the weighing scale 25. The mass of thefluid-saturated sample without the surrounding fluid in the weighingfluid, m_(f), may be given by the formula

m _(f) =V _(m)ρ_(m) +V _(ϕ)ρ_(l) −V _(c)ρ_(f)

where ρ_(f) is the density of the weighing fluid. The computerexecutable instructions may also trigger the computer to determine avolume of the fluid-saturated sample without the surrounding fluid,V_(c), using the formula

V _(c)=(m _(s) −m _(f) −V _(sur)ρ_(l))/ρ_(f).

The computer executable instructions may further trigger the computer todetermine a bulk density of the fluid-saturated sample without thesurrounding fluid, ρ_(b), using the formula

$\rho_{b} = {\frac{{V_{m}\rho_{m}} + {V_{\varphi}\rho_{l}}}{m_{s} - m_{f} - {V_{sur}\rho_{f}}}{\rho_{f}.}}$

The computer executable instructions may further trigger the computer todetermine the volume of the matrix, V_(m), using the formula

V _(m)=(m _(s) −m _(f) −V _(sur)ρ_(f))/ρ_(f) −V _(ϕ).

The computer executable instructions may further trigger the computer todetermine the matrix or grain density of the subsurface formation,ρ_(m), using the formula

$\rho_{m} = {\frac{m_{s} - {\left( {V_{\varphi} + V_{sur}} \right)\rho_{f}}}{{\left( {m_{s} - m_{f} - {V_{sur}\rho_{f}}} \right)/\rho_{f}} - V_{\varphi}}.}$

While the invention has been described with respect to a limited numberof embodiments, those skilled in the art, having benefit of thisdisclosure, will appreciate that other embodiments can be devised whichdo not depart from the scope of the invention as disclosed herein.Accordingly, the scope of the invention should be limited only by theattached claims.

1. A system for characterization of a subsurface formation, the systemcomprising: a fluid-saturated sample of a subsurface formation; abalance configured to receive the fluid-saturated sample and output thein-air mass of the fluid-saturated sample; a computer comprising one ormore processors and a non-transitory computer readable medium comprisingcomputer executable instructions that when executed by the one or moreprocessors, trigger the computer to: receive in-air mass of afluid-saturated sample of the subsurface formation, wherein the in-airmass comprises mass of the sample, mass of a fluid surrounding thesample, and mass of the fluid inside the sample, the in-air mass of thefluid-saturated sample, m_(s), given by the formula:m _(s) =V _(m)ρ_(m)+(V _(ϕ) +V _(sur))ρ_(l) where ρ_(m) is a density ofthe matrix of the subsurface formation, ρ_(l) is a density of the fluidinside and surrounding the sample, V_(m) is a volume of the matrix,V_(ϕ) is a volume of the fluid inside the sample, and V_(sur) is avolume of the fluid surrounding the sample; determine volume of thefluid inside the sample, V_(ϕ), and volume of the fluid surrounding thesample, V_(sur), using nuclear magnetic resonance (NMR); receive mass ofthe fluid-saturated sample in a weighing fluid; determine mass of thefluid-saturated sample without the surrounding fluid in the weighingfluid, m_(f), given by the formulam _(f) =V _(m)ρ_(m) +V _(ϕ)ρ_(l) −V _(c)ρ_(f) where ρ_(f) is the densityof the weighing fluid; and determine a volume of the fluid-saturatedsample without the surrounding fluid, V_(c), using the formulaV _(c)=(m _(s) −m _(f) −V _(sur)ρ_(l))/ρ_(f).
 2. The system of claim 1,wherein the computer executable instructions further trigger thecomputer to: determine a bulk density of the fluid-saturated samplewithout the surrounding fluid, ρ_(b), using the formula$\rho_{b} = {\frac{{V_{m}\rho_{m}} + {V_{\varphi}\rho_{l}}}{m_{s} - m_{f} - {V_{sur}\rho_{f}}}{\rho_{f}.}}$3. The system of claim 2, wherein the computer executable instructionsfurther trigger the computer to: determine volume of the matrix, V_(m),using the formulaV _(m)=(m _(s) −m _(f) −V _(sur)ρ_(f))/ρ_(f) −V _(ϕ).
 4. The system ofclaim 3, wherein the computer executable instructions further triggerthe computer to: determine matrix or grain density of the subsurfaceformation, ρ_(m), using the formula:$\rho_{m} = {\frac{m_{s} - {\left( {V_{\varphi} + V_{sur}} \right)\rho_{f}}}{{\left( {m_{s} - m_{f} - {V_{sur}\rho_{f}}} \right)/\rho_{f}} - V_{\varphi}}.}$